13 citations · 15 across the 7 of their papers we have counts for
12 papers
Gaussian rigidity and width of measures
Alessandro Pigati
Given and a positive Radon measure on with at most polynomial growth, assume that it has finite -dimensional Gaussian discrepancy, defined as $$\mat…
Scale-invariant bounds on thin sets for measures satisfying a first-order PDE and the anisotropic Michael-Simon inequality
Guido De Philippis, Luca Gennaioli, Alessandro Pigati +1
We prove mass estimates for PDE-constrained measures on sets of -finite -measure, assuming an appropriate rank condition. As an application, we derive a Michael-…
Michael-Simon inequality for anisotropic energies close to the area via multilinear Kakeya-type bounds
Guido De Philippis, Alessandro Pigati
Given an anisotropic integrand , we can generalize the classical isotropic area by looking at the functional $$\mathcal{F}(Σ^k):=\int_ΣF(T…
Nonabelian Yang-Mills-Higgs and Plateau's problem in codimension three
Davide Parise, Alessandro Pigati, Daniel Stern
We investigate the asymptotic behavior of the -Yang-Mills-Higgs energy in the large mass limit, proving convergence to the codimensi…
Decay of excess for the abelian Higgs model
Guido De Philippis, Aria Halavati, Alessandro Pigati
In this article we prove that entire critical points of the self-dual -Yang-Mills-Higgs functional , with energy $$E_1(u,\nabla;B_R):=\int_{B_R}\left[|\nabl…
The Parabolic -Higgs Equations and Codimension-two Mean Curvature Flows
Davide Parise, Alessandro Pigati, Daniel Stern
We develop the asymptotic analysis as for the natural gradient flow of the self-dual -Higgs energies $$E_ε(u,\nabla)=\int_M\left(|\nabla u|^2+ε^2|F_{\nabla}|^2+\frac…
Non-degenerate minimal submanifolds as energy concentration sets: a variational approach
Guido De Philippis, Alessandro Pigati
We prove that every non-degenerate minimal submanifold of codimension two can be obtained as the energy concentration set of a family of critical maps for the (rescaled) Ginzburg-L…
Quantization and non-quantization of energy for higher-dimensional Ginzburg-Landau vortices
Alessandro Pigati, Daniel Stern
Given a family of critical points for the complex Ginzburg--Landau energies \begin{align*} &E_ε(u)=\int_{M}\left(\frac{|du|^2}{2}+\frac{(1-|u|^2)^2}{4ε^2}\ri…
Convergence of the self-dual -Yang-Mills-Higgs energies to the -area functional
Davide Parise, Alessandro Pigati, Daniel Stern
Given a hermitian line bundle on a closed Riemannian manifold , the self-dual Yang-Mills-Higgs energies are a natural family of functionals \begin{align*} &E_ε(u,…
The viscosity method for min-max free boundary minimal surfaces
Alessandro Pigati
We adapt the viscosity method introduced by Rivière to the free boundary case. Namely, given a compact oriented surface , possibly with boundary, a closed ambient Riemannian man…
Minimal submanifolds from the abelian Higgs model
Alessandro Pigati, Daniel Stern
Given a Hermitian line bundle over a closed, oriented Riemannian manifold , we study the asymptotic behavior, as , of couples critical for the…
Free boundary minimal surfaces: a nonlocal approach
Alessandro Pigati, Francesca Da Lio
Given a -smooth closed embedded manifold , with , and a compact connected smooth Riemannian surface with $\partial S\neq\emptys…